Question

Stella is a salesperson who sells computers at an electronics store. Let P represent Stella's total pay on a day on which she sells x dollars worth of computers. A graph of P vs. x is shown below. Write an equation for P, then state the y-intercept of the graph and determine its interpretation in the context of the problem.

a) P = mx + b, y-intercept = b, representing Stella's base pay.
b) P = mx + b, y-intercept = m, representing Stella's commission rate.
c) P = bx + m, y-intercept = b, representing Stella's commission rate.
d) P = bx + m, y-intercept = m, representing Stella's base pay.

Answer 1

The correct equation for Stella's total pay P is P = mx + b, where b is the y-intercept representing Stella's base pay and m is the slope representing her commission rate based on sales.

Step-by-step explanation:

The equation for Stella's total pay P based on the amount x dollars worth of computers she sells can be represented by the linear equation P = mx + b, where m is the slope of the line representing the commission rate, and b is the y-intercept representing the base pay or the guaranteed pay that Stella earns regardless of her sales.

From the options provided, the correct choice is a) P = mx + b, y-intercept = b, representing Stella's base pay. This means that when x is 0, that is, when Stella does not make any sales, her total pay P would still be b, indicating her guaranteed minimum income or base pay.

Therefore, in the context of the problem, the y-intercept b is particularly significant as it represents the amount that Stella would earn as base pay without selling any computers.